Bank-Borrower Relationships and Transition from Joint Liability to Individual Liability
Loans in Microcredit
Sugato Chakravarty
Department of Consumer Sciences, Purdue University
812 West State Street, West Lafayette, IN 47907, USA
Email: sugato@purdue.edu
Phone: (01) 765-494-8296
Fax: (01) 765-494-0869
Abu Zafar M. Shahriar
Department of Accounting and Finance, Monash University
Room 45, Level 3, Building H, 900 Dandenong Road
Caulfield East, Victoria 3145, Australia
Email: shahriar.abuzafar@monash.edu
Phone: (61) 0449002243.
November 2012
1
BANK-BORROWER RELATIONSHIPS AND TRANSITION FROM JOINT LIABILITY
TO INDIVIDUAL LIABILITY LOANS IN MICROCREDIT
Abstract
We use primary data from Bangladesh to examine whether the strength of bank-borrower
relationships affects the process of a borrower’s transition from joint liability to individual
liability loans in microcredit. Using a survival analysis framework, we show that borrowers
who maintain non-mandatory savings accounts with their microfinance institutions (MFIs),
and those who borrow from a single MFI (i.e., do not have banking relationships with
multiple MFIs), graduate from joint liability to individual liability loans with a relatively
short repayment history. Our findings imply that MFIs have incentives to invest in
relationship development with their clients in order to expedite the process of a borrower’s
transition from group to individual loans which, in turn, can reduce the incidence of voluntary
drop-outs by mature borrowers.
2
1. Introduction
Microfinance institutions (MFIs) in Bangladesh extend group loans, with a joint
liability clause, to most of their new clients. 1 Many of these borrowers, however, graduate to
individual loans over time. For example, every year, 10-15 percent of the group borrowers of
BURO (Basic Unit for Resources and Opportunities—an MFI based in Bangladesh) graduate
to individual loans (see for example, BURO, 2007). Similar evidence is found in Bangladesh
Rural Advancement Committee (BRAC), where borrowers graduate to individual loans after
completing a few cycles of joint liability loans. In this paper we examine whether the strength
of bank-borrower relationships affects the process of a borrower’s transition from joint
liability to individual liability loans in the microcredit sector. The special nature of bankborrower relationships has been the subject of extensive research in finance.2 One major
benefit of relationship banking is that it creates room for flexibility in loan contracts that
permits the utilization of subtle and non-contractible information (Boot, 2000). This paper
contributes to this literature by showing evidence that relationship driven soft information
substitutes for the need for joint liability in microcredit contracts and, thereby, expedites the
process of a borrower’s transition from joint liability to individual liability loan.
Although there exist a large number of theoretical and empirical papers on
relationship banking, there is a distinct paucity of empirical research that substantiates the
role that bank-borrower relationships might play in the microcredit sector. To the best of our
knowledge, the study by Chakravarty and Shahriar (2011) is the lone exception. The present
study, however, differs from the existing literature in that while Chakravarty and Shahriar
(2011) provides evidence that the strength of banking relationships affects the availability of
microcredit in Bangladesh, we focus on whether banking relationships might affect specific
contractual features related to microloans. We do so using primary data compiled from 34
1
Although some MFIs, such as the Association for Social Advancement (ASA—a large MFI in Bangladesh),
provide individual loans only, lending with a joint liability contract is the most common form of micro-lending
in Bangladesh. Under a joint liability contract, potential borrowers form groups and collectively apply for loans.
If the loan application is approved, each member of the group individually receives a loan but the entire group
remains jointly responsible for repayment. Thus, if one borrower fails to repay, her group members are
contractually required to repay in her stead. Such repayments are enforced through the threat of denial of future
credit to all members of the defaulting group, or by drawing on a group fund that serves as collateral (Fischer
and Ghatak, 2011).
2
Relationship banking refers to the process of multiple interactions between a borrower and a lender over time.
Through relationship banking the lender gathers borrower-specific information, which is not publicly available
and is proprietary in nature. Prior studies have identified several potential benefits of relationship banking. See,
for example, Bharath et al. (2007 and 2011), Berger and Udell (1995, 2002), Chakravarty and Scott (1999),
Chakravarty and Yilmazer (2009), Cole (1998), Cole et al. (2004), and Petersen and Rajan (1994).
3
randomly selected villages in Bangladesh. Our sample includes 334 active micro-borrowers,
who either graduated from a joint liability to an individual liability loan within one year prior
to the survey, or still had a joint liability loan when the survey was conducted in 2009. Other
details pertaining to the data collection process are provided in section 4. In order to examine
whether a strong bank-borrower relationship expedites the process of a borrower’s transition
from joint to individual liability loans, we applied a survival analysis model the details of
which are provided in section 5.
The results from our empirical analysis show that (a) borrowers who maintain a nonmandatory savings account3 with their MFI, graduate sooner to individual loans than those
who do not have such accounts, and (b) those who borrow from a single MFI, graduate
sooner to individual loans than those who simultaneously borrow from multiple MFIs. We
also estimate the role of relationships using an instrumental variables (IV) technique in order
to better address a potential endogeneity problem.4 The use of the IV method makes it
credible to assert that there is a causal relationship between bank-borrower relationships and
the process of transition from joint liability to individual liability loans.
Microfinance loan officers view voluntary drop outs (from the credit program), by
their mature (in terms of their borrowing history) borrowers, as a serious problem (see for
example, Wright, 2000 and 2001; and Meyer, 2002). New borrowers typically have smaller
loans compared to existing borrowers, and they (the new borrowers) need training to get
familiar with the rules and regulation of the MFIs. Thus, borrower drop outs increase the
training and administrative costs of the MFIs. Current research also shows that the presence
of the joint liability feature in the loan contract is a major reason for voluntary drop outs by
the mature borrowers.5 The results of our study suggest that a strong banking relationship
expedites the process of a borrower’s graduation from joint to individual liability loans. This,
in turn, is expected to reduce voluntary drop outs by the mature borrowers, who do not like
joint liability and seek greater flexibility associated with individual loan contracts. Thus, an
implication of our findings is that both the borrowers and the lenders in the microcredit sector
3
Borrowers from most of the MFIs in Bangladesh have to maintain a mandatory savings account in order to
receive a micro loan. In addition to the mandatory savings, MFIs offer other non-mandatory savings schemes to
their clients.
4
We discuss the potential endogeneity problem and the choice of instrumental variables in detail in section 6.
5
In 1995, the field staff of ASA conducted a study to identify the factors that drive the decision to exit
microcredit programs (ASA, 1996). It has been found that the presence of joint liability in the loan contract is
one of the main causes behind voluntary drop outs. Furthermore, based on information from secondary sources,
Wright (2001) shows that more than 60 percent of the borrowers who drop out voluntarily from BRAC, do so
because they do not like joint liability. Similar evidence is found in the Women’s World Banking Report (2003).
4
have incentives to invest in relationship development in order to expedite the transition to
individual loans.
The remainder of this paper is structured as follows: In section 2, we review the
background literature. In section 3, we develop a simple model to formalize the effect of
bank-borrower relationships in the transition from joint to individual loans. In section 4, we
describe the data and variables. In section 5, we construct our empirical framework. In
section 6, we present the findings of our empirical analysis. Finally, we conclude in section 7.
2. Background Literature
The theoretical literature on microcredit suggests that joint liability can mitigate
adverse selection and moral hazard problems in the rural credit markets (see for example,
Stiglitz, 1990; Varian, 1990; Ghatak and Guinnane, 1999; Armendariz de Aghion, 1999; and
Ghatak 1999 and 2000). In fact, there is a widespread consensus among the researchers and
policy makers in that it is the “discovery” of joint liability that made microcredit popular
around the world (Armendariz de Aghion and Morduch, 2010). The recent trend in
microcredit, however, suggests that, in spite of its apparent attractiveness, joint liability is
losing popularity as the microfinance community is increasingly being aware of the hidden
costs associated with such contracts (see, for example, Gine and Karlan, 2010).
Joint liability imposes a hidden cost to the borrowers as they have to bear the added
responsibility of repaying the defaulting group member’s loans. Furthermore, although some
researchers (see for instance, Stiglitz, 1990) have assumed that peer monitoring is a costless
byproduct of living in close proximities, in practice, however, peer monitoring is not costless
no matter how close the group members live (Armendariz de Aghion, 1999). Finally,
imposing social sanctions on the defaulting group members under joint liability contracts is
costly as it deteriorates the development of social capital in the long run. Thus, it is not
surprising to see why more than 70 percent of the group borrowers of the Women’s World
Banking affiliates in Bangladesh and Uganda revealed their preference for individual loans
(Women’s World Banking, 2003).
Additionally, the joint liability feature imposes hidden costs on the lenders because it
may deteriorate their clients’ incentives to repay their loans. First, a borrower’s reliance on
fellow group members to repay loans opens the door to free riding, causing the default rates
to rise (Abbink, Irlenbusch, and Renner, 2006). Second, if within a group, one member’s
project succeeds and the others’ fail, the former (who may have otherwise repaid under
5
individual contracts) may decide to default strategically, (see, for example, Besley and Coate,
1995; and Paxton, Graham, and Thraen, 2000). All of these factors may help explain why
many major microfinance institutions have recently expanded into, or converted their
portfolios to, individual liability loans (Armendariz de Aghion and Morduch, 2010). The
current study, however, differs from this literature in that while previous research has
primarily focused on the merits and demerits of joint liability over individual liability loans,
we focus on the question of how, over time, micro-borrowers might graduate from one kind
of loan to the other.
Several studies have examined similar graduation processes in the conventional credit
markets. Notable examples are Diamond (1991) and Boot and Thakor (1994). Diamond, for
instance, theorizes that new firms borrow from banks until they establish a good reputation in
the credit market by repaying the monitored loans. Since reputation is a valuable asset, firms
that build reputation have an incentive to protect it. As a result, these firms show greater
prudence in their investment decisions, reducing the moral hazard problem and the associated
credit risks faced by the bank. Diamond assumes that borrower’s reputation is portable. Thus,
borrowers can use their reputation in the private debt market to secure low-cost financing
from the public debt market. In Boot and Thakor’s model, new borrowers get secured loans
from banks with above-market borrowing costs. Once these borrowers develop a reputation
by repaying loans, they are offered loans at below-market borrowing costs without any
collateral.
We argue that a similar reputation effect may be at play in the process of graduating
from joint to individual liability loans in the microcredit sector. So, for instance, when an
MFI extends group loans to its new clients, group members monitor each other’s activities
and exert pressure on those who misuse their funds. However, when these borrowers
successfully complete a few loan cycles and establish a good reputation, they invest funds
diligently in their own interest, and without any peer pressure. They do so in order to protect
their valuable reputational capital, which can be used as a certification measure in the credit
market. The MFIs then extend individual loans to these borrowers without increasing their
credit risks.
It is, however, worth underscoring that in both of the above mentioned models, the
development of reputational capital depends on the length of an uninterrupted repayment
record. When a lender is uncertain about a borrower’s type, the repayment of a loan revises
upward the lender’s belief about the creditworthiness of the borrower. As a result, borrowers
with good repayment records receive loans with flexible terms and conditions. In the context
6
of microcredit, if the reputational capital (as evidenced by the borrower’s uninterrupted
repayment record) is the only factor that affects the transition from joint to individual liability
loans, we should observe a certain threshold number of loan cycles after which every
borrower would graduate from joint to individual liability loans. This is due to the fact that
microloans in Bangladesh are typically extended with a fixed one year-contract, and that
borrowers lose access to all kind of future loans from the same lender upon one single default.
In practice, however, we are not aware of any such fixed threshold number of loan cycles,
which implies that some borrowers receive individual loans with a relatively shorter
repayment track record than others. For example, the length of repayment record that the
group borrowers of BURO Bangladesh require to graduate to individual loans varies from
one to eight years (BURO, 2007).6 This implies that the magnitude of reputation effect (on
the likelihood of transition form joint liability to individual liability loans) varies from client
to client in the microcredit sector.
In the context of the conventional credit markets, Vercammen (1995) has shown that
the magnitude of the reputation effect depends on the availability of information about a
borrower’s type. When a bank has little to no information about the borrower’s type, it relies
substantially on the value of the reputational capital, evidenced by the borrower’s repayment
record, in order to offer any flexibility in the loan contract. However, as client-specific
information is generated over time, the importance of reputation gradually declines in
updating the lender’s belief about the borrower’s type. In the limiting case, when the lender
has perfect information about a borrower’s type, the reputation effect may disappear
altogether. The typical clientele of microcredit lack formal certification measures to offer to
the lenders. For example, their clients do not have credit scores nor do they have formal
financial statements. Moreover, they cannot offer assets to pledge against their loans.
Therefore, the MFIs cannot collect client-specific information using conventional
transactions-based methods.7 Based on evidence from Bangladesh, Chakravarty and Shahriar
(2011) have shown that, in the absence of transactions-based lending technology, MFIs rely
substantially on lending relationships in extending loans. In relationship based lending,
lenders invest in developing close ties with their borrowers, which produce valuable clientspecific information of the type that is not readily observed (i.e., soft). Such information
6
Copestake (2002) shows similar evidence that some group borrowers in the Zambian microcredit sector
graduate sooner to individual loans than the others.
7
In the transactions-based technology, lenders collect information from the borrower’s credit scores, financial
statements, and the amount of assets offered as collateral (Berger and Udell, 2002).
7
serves to predict future repayment behavior of the borrower without joint liability. Thus, we
expect that borrowers with stronger relationship metrics might require a shorter repayment
record to graduate to receiving an individual loan. This is the testable implication of the
current paper, and is the focus of our empirical analysis. The next section formally develops
the testable hypotheses.
3. The Model
Following Ghatak (2000), we consider a simple model of a competitive credit market
where the lending side is represented by many profit maximizing MFIs and the borrowing
side is represented by many utility maximizing borrowers.8 Each borrower has one unit of
labor and needs one unit of capital to invest in a project. Borrowers lack sufficient wealth and,
therefore, need to borrow from the MFIs to launch projects. Upon receiving a loan, a
borrower can undertake any one of the two projects: a relatively safe project that yields, if
successful, a return of YS; and a relatively risky project that yields, if successful, a return of
YR. If a project fails, the return is zero. The probability of success for each project is PS and
PR, where
0 < PR < PS < 1
(1)
Following Stiglitz and Weiss (1981), we assume that safe and risky projects have the
same mean return, but risky projects have a greater spread around the mean.9 That is,
PS YS = PR YR
(2)
We further assume that the project outcome (success or failure) is independently distributed
for the same type as well as across different types of borrowers.
Borrowers do not have any formal certification measures, such as credit history or
financial statements, to prove their creditworthiness in the loan application stage.
Furthermore, the investment project chosen by a borrower, in the loan utilization stage, is not
8
Specifically, we modify Ghatak’s model to capture the effects of reputational capital in the microcredit sector.
9
When this assumption holds, the credit market is characterized by an under investment problem, where lenders
ration credit. In contrast, De Meza and Webb (1987) assume that both the safe and risky projects yield the same
return when successful, but the risky projects have lower mean returns than the safe projects. Under this latter
assumption, the credit market is characterized by an over investment problem because the risky borrowers are
subsidized by the safe borrowers. It is worth underscoring that these two distinct assumptions can lead to
different outcomes in the credit market. However, since existing evidence suggests that there is an unmet need
for microcredit (see for example, Evans, Adams, Mohammed and Norris, 1999; and Meyer, 2002), we assume
that there is credit rationing in this market. Our specific assumption therefore follows naturally.
8
observed by the MFI. That is, the credit market is characterized by both adverse selection and
moral hazard problems. The use of collateral—a common solution to address information
problems—is not feasible as the borrowers do not have any assets to pledge their loans. An
MFI does two things under such a situation. First, it treats all borrowers identically and offers
the same loan contract. Second, it adopts indirect mechanisms to address the information
problems such that, when a borrower accepts the loan contract, she chooses specific actions
in her own interest that serves to reduce the probability of default. One such mechanism
offered by a lender is to offer credit under a joint liability contract. However, due to the
hidden costs associated with joint liability, both the MFI and the borrowers prefer individual
loans. But since individual loans do not induce any indirect mechanisms to address the
information problems, such as peer screening and peer monitoring, initially the MFI offers
only joint liability loans to all its borrowers. This leaves the borrowers with two options: they
can either accept a joint liability loan contract, or they can reject the offer and forgo a
valuable investment opportunity.
Once the borrowers accept a joint liability loan contract, they form homogeneous risk
groups using locally available information through a mechanism known as positive
assortative matching (see, for example, Siglitz, 1990; and Ghatak, 1999 and 2000). That is,
borrowers who have access to safe investment projects form groups among themselves
leaving those with risky projects to form groups with similar risk-type partners.10
Repayment of a loan is a function of project outcome. Thus, if the project of a specific
borrower fails, she cannot make any repayment as she lacks sufficient wealth to do so. If a
borrower is unable to make repayment, and as a result, the loan is overdue for more than a
year, the loan is declared as a ‘bad loan’ by the MFI, against which 100 per cent provision is
to be made.11 In our model, a borrower, whose loan has been declared as a bad loan, is said
to have defaulted on her loan. It is worth underscoring that, typically, no further loan is
extended to such borrowers by the same MFI. We assume that the outcome of a project of a
borrower is observable and verifiable by the MFI at no cost. Moreover, the costs to enforce
10
Prior research has shown that heterogeneous risk groups may also emerge in microcredit if group members
transfer resources among themselves for purposes of risk sharing (see for example, Sadoulet, 1999; Sadoulet and
Carpenter, 2001; and Chakravarty and Shahriar, 2011(b)). In the present model, however, we do not introduce
intra-group resource transfer, and thus, rule out the possibility of heterogeneous group formation.
11
This guideline is provided by the Microcredit Regulatory Authority of Bangladesh (see, for example, MRA,
2012) as a regulatory requirement.
9
repayment (if a project succeeds) are negligible. Thus, we rule out the possibility of strategic
default by the borrowers.
If, on the other hand, the project is successful, the borrower makes a repayment of r >
0 to the MFI. Due to the joint liability clause, if the project of a specific borrower succeeds
and that of one (or more) of her partners fails, in addition to her individual liability payment,
r, the borrower is contractually required to pay a joint liability payment in order to bail out
her defaulting peer(s). By the same token, if the project of a borrower fails but that of her
partners succeed, she is bailed out by her peers. If a borrower fails to repay her loan, her
borrowing partners, as a group, have to contribute c in order to bailout their defaulting partner.
Here, c is constant for a given loan size, interest rate, and other service charges.
Upon successful repayment of a loan, a borrower accumulates a reputation in the
credit market, which can be used as a certification measure of her creditworthiness in the
future. Let V represent the present value of future rents from such reputational capital, which
depends on the length of an uninterrupted repayment record, l. When a borrower does not
have any repayment record (i.e., when l = 0), the value of reputational capital is also zero.
The value of reputation, however, increases with successful repayment of loans. Thus, as the
length of repayment record increases, the value of V also goes up at a decreasing rate (i.e.,
′
0and
′′
0).
We can now derive the expected payoff function of a borrower. Let us consider a
borrower who invests in a safe project. Through the mechanism of positive assortative
matching, she forms group with N borrowing partners, all of whom invest in safe projects
(this implies a borrowing group of size N +1). Under a joint liability contract, if a borrower
invests in a safe project, her expected payoff is given by:
∑
1
1
∑
1
(3)
Equation (3) captures all possible combinations of a borrower’s payoff—starting from
the case where all the members of a group successfully repay their loans to the case where all
the members fail to make a repayment. In appendix A, we provide an example where the
borrowing group consists of three members.
The first part of the right hand side of equation (3) denotes the payoff of the borrower
when her project is successful (which happens with a probability ), and the second part
denotes the payoff when her project fails (which happens with a probability1
10
). In both
cases, i denotes the number of borrowing partners whose projects are successful, irrespective
of the borrowers’ own project status. Thus, if i = 2, for example, it means two out of N
partners of the borrower have succeeded.
If the project of the borrower succeeds, it yields . In this case, the borrower repays
her individual liability payment (r) to the bank and, in return, gains V in terms of reputational
capital. In addition, the borrower needs to repay a joint liability payment to bailout her
defaulting peers. We assume that, if successful, a project yields sufficient return to make both
the individual and joint liability payments (i.e., YS ≥ r + Nc)12. The joint liability payment to
bail out the defaulting peers in a group, however, is split equally among the successful
members of the group. Thus, the borrowers’ share of joint liability payment is given
by
⁄ 1
. If the project of the borrower fails, it does not yield any return, and the
borrower does not repay the individual liability component of her loan. Moreover, in this case,
she does not contribute to bailing out any defaulting peer. But if at least one of her partners
succeeds, the successful partner makes repayment on her behalf due to the joint liability
clause of the loan contract. This raises the value of her reputation to the lender by V. This
indicates a noteworthy feature of a joint liability contract. Under such contracts, if a borrower
fails to make any repayment but her borrowing partners make repayment on her behalf, she
(the defaulting member of the group) still accumulates a good reputation in the credit market
because, at the end of the day, the MFI only cares about overall repayment of a borrowing
group which is captured in the second part of the right hand side of equation (3). This is due
to the fact that when the project of the borrower fails, i = 0 implies that none of the members
of her group would repay on her behalf, and thus, the borrower would not gain anything in
terms of reputational capital (i.e., V = 0).
Similarly, we can derive the expected payoff of a borrower when she (and her partners)
invests in a risky project as follows:
∑
1
∑
1
1
In this framework, a borrower will invest in a safe project only if
(4)
. In a group
of two borrowers, this can be reduced to the following condition:
1
1
1
1
12
This is also true with the risky projects, i.e., YR ≥ r + Nc 11
(5)
By solving this inequality condition, we find that a borrower invests in a safe project
only if the following condition is met:
(6)
2
Our model depicts a competitive credit market, where the lending side is
characterized by many profit maximizing MFIs. Suppose an MFI’s opportunity cost of capital
is given by ρ. The zero profit constraint of the MFIs requires that the expected repayment
from each loan be equal to the opportunity cost of capital. Let us denote (r, c) as the contract
that satisfies the zero profit condition for both safe and risky borrowers. That is, (r, c)
satisfies the following conditions in a group of two members:
1
(7)
1
(8)
By solving equations (7) and (8), we get:
(9)
1
Equation (9) implies that if r >0, in order to rule out a negative joint liability payment,
1
we must have
that
2
0. 13 Furthermore, the assumption that 0 < PR < PS < 1implies
0. These two conditions together imply that for a given value of r, c is
decreasing in V. Therefore, for a sufficiently large value of reputational capital, the MFI can
set c = 0 and still make sure that the loans are invested in safe projects. Particularly, when V
= kr, where k =1⁄ 2
, is some constant, the MFI can remove the joint liability
feature altogether from the loan contract. To understand the intuition behind this, suppose a
borrower enters the credit market and receives her first joint liability loan at period t = 0. This
new borrower is not afraid of losing reputation in the credit market because she has not yet
established any (i.e., V = 0). Therefore, she may lack an incentive to invest in a safe project
in order to increase the likelihood of repayment. Accordingly, the MFI sets c > 0 (i.e., it
extends loans with joint liability) so that the borrower feels peer pressure from her group
members to invest in a safe project. However, once this borrower establishes a certain
threshold level of reputation (i.e., V = kr), she invests in a safe project on her own interest,
13
Ghatak (2000) assumes similarly in his study.
12
without the need for any peer pressure, in order to protect her valuable reputation by
decreasing the likelihood of default. At this point, the MFI can offer her individual loans
without increasing credit risk. Let us denote this threshold level of reputation as . As
mentioned earlier, the value of reputation in the credit market depends on the length of an
uninterrupted repayment record. Suppose ̅ denotes the length of repayment record that a
borrower needs in order to accumulate the threshold level of reputation, .
̅
Anecdotal evidence, however, suggests that the value of —in
other words, the
magnitude of the reputation effect—varies from borrower to borrower within the same MFI.
As we mentioned earlier, the magnitude of a reputation effect in the credit market depends on
how much information the lender has about a borrower’s creditworthiness. Borrowers who
have a strong relationship with their bank are informationally more transparent, which leaves
room for the lender to make changes in loan terms. As a result, the transition from joint to
individual liability loans might be fast-tracked for such borrowers.
In order to capture for the strength of banking relationships, prior research has
suggested looking at the number of financial services that a borrower receives from a bank
(see for example, Berger and Udell, 1995; and Chakravarty and Scott, 1999). A typical MFI
in Bangladesh provides two major financial services, other than credit, to its clients—savings
and insurance. While having a mandatory savings account is a pre-requisite for applying for
microcredit in most cases, having a non-mandatory savings account is indeed a choice
variable. Accordingly, we introduce (the maintenance of) a non-mandatory savings account
as a relationship proxy. Buying insurance, however, is not a pure choice variable. Insurance
schemes are available only beyond a certain threshold level of loan. As a result, we choose to
not include (the purchase of) insurance as a relationship variable. By maintaining savings
accounts that are not prerequisites to receive loans, borrowers reveal information about their
financial strength and fiscal discipline. Thus, MFIs may offer individual loans to those who
have maintained a non-mandatory savings account with a relatively shorter repayment record.
This leads us to the first testable proposition of the paper.
Proposition (a): Borrowers who maintain a non-mandatory savings account
are likely to graduate sooner from joint to individual liability loans compared
to those who do not have such accounts with their MFI.
A common feature of microcredit is the so-called progressive lending, where
borrowers have the option of receiving a larger loan upon successful repayment of a given
loan. Default on any single loan, on the other hand, terminates the lending relationship. In the
13
absence of any legal mechanism to induce repayment, this “carrot” works as a major
borrower disciplining device. However, if a borrower has loans from multiple MFIs, the
threat of denial of future credit loses its teeth. Hence, the MFIs always prefer to lend to those
who have associations with a single MFI (see, for example, Meyer, 2000). These borrowers
(with single banking relationships) are more inclined to maintain a long term relationship
with their MFIs in order to ensure an uninterrupted supply of bank loans. As a result, they are
more likely to invest in a safe project to enhance the likelihood of repayment, irrespective of
the lending methodology. Therefore, MFIs may offer individual loans to these clients with a
relatively shorter repayment record. This leads us to the second testable proposition.
Proposition (b): Clients who borrow from a single MFI are likely to graduate
sooner from joint to individual liability loans compared to those who borrow
from multiple MFIs.
4. Data and Variables
We use a data set that was compiled based on a household survey of 34 randomly
selected villages conducted in Bangladesh over the summer of 2009.14 A multi-stage
sampling method was used to select the specific villages to survey. In the first stage, the
following six districts were chosen randomly from the six administrative divisions of the
country in order to collect data from a representative sample: Mymensingh, Rajshahi,
Meherpur, Barisal, Maulavibazar and Chittagong. 15 In the second stage, two counties were
selected from each of the six districts as follows. First, all of the counties in each district were
ranked based on population density, but only after excluding counties that are part of district
headquarters, or other municipality areas, in order to avoid urban population.16 Next, one
14
Chakravarty and Shahriar (2011) have used the same data set.
15
In 2009, Bangladesh was divided into six administrative divisions. The six divisions were divided into 64
districts, 491 counties or sub-districts, and 4,498 unions—a union being the lowest administrative unit in the
rural areas, consisting of a group of villages. However, in early 2010, the old Rajshahi division was divided into
two divisions: Rangpur and Rajshahi. Accordingly, there are now seven administrative divisions in Bangladesh.
16
The theoretical models on group lending described above are based on a crucial assumption that the group
borrowers have the necessary information on each other, which they exploit in forming groups and obtaining
loans. This assumption, although appropriate in the rural areas of Bangladesh, is often violated in the urban
settings where people living in close proximity do not know each other well. Laffont and N’Guessan (2000)
provide evidence that when group members do not know one other, the collateral effect of group lending does
not work. Therefore, we felt that including urban settings in our survey design would introduce noise in the data
without an obvious upside.
14
county was randomly selected from those that had more than the median population density,
and one was randomly selected from those that had less than the median population density.
In the third stage, one union was randomly selected from each of the 12 counties but only
after excluding unions that are part of county headquarters. In the fourth stage, three villages
were randomly selected from each of the 12 unions. The only exception was Meherpur
district, where 2 villages were randomly selected from each county. More detailed on the
sampling method has been discussed in Chakravarty and Shahriar. Our sample includes 334
active micro-borrowers (i.e., they had ongoing loans with the MFI when the survey was
conducted). Out of these 334 borrowers, 82 graduated from joint to individual liability loans
within one year prior to the survey. The rest 252 borrowers started with joint liability loans
and still had the same when the survey was conducted.
A noteworthy feature of micro-lending in Bangladesh is that if a borrower defaults on
a loan obligation (i.e., if a loan is overdue for more than a year), no further loan is extended
to that borrower, and as a result, the banking relationship between the borrower and the MFI
is terminated. Therefore, for active micro-borrowers, the length of membership with their
MFIs can be used as a proxy for the length of an uninterrupted repayment record. In our
survival analysis model, for borrowers who graduated to individual loans, the length of
membership is measured at the point they received their first individual loan, as a proxy for
the length of repayment record that the borrowers needed to graduate. For the borrowers who
did not graduate (i.e., who still had a group loan), the length of membership is measured at
the point they received their most recent joint liability loans as a proxy for the length of
repayment record. The explanatory variables that are of primary interest in this study are
those which measure the strength of bank-borrower relationships in the microcredit sector.
We use two particular measures to estimate the strength of banking relationships for a given
borrower— maintenance of a non-mandatory savings account and the presence of a single
banking relationship.
We are unaware of any theoretical or empirical study, which can guide to choose the
set of control variables that might affect the timing of transition from joint to individual
liability loans in microcredit. Armendariz de Aghion and Morduch (2010), however, identify
some borrower, MFI, and community specific features that distinguish group loans from the
individual loans. Based on evidence from 74 group and 73 individual lending programs
across the world, they have for instance, shown that (a) MFIs are more likely to extend
individual loans to their relatively well-off clients; (b) individual loans are more common in
sparsely populated regions; and (c) MFIs using individual lending methodology tend to be
15
smaller in size (in terms of outreach). We expect that the same factors might affect the
process of transition from joint to individual liability loans. We have also introduced the
frequency of repayment as a control variable in our survival analysis. Typical microcredit
contracts require weekly repayment of loans in small installments. Although frequent
repayment schedule increases the transaction costs, MFI loan officers believe that it is critical
for the success of their programs (see for example, Yunus, 2004).17 The expected impact of
repayment frequency on the process of transition, however, is not clear. On one hand,
microfinance practitioner’s belief that a less frequent repayment schedule (for example, biweekly or monthly, as opposed to weekly) may increase delinquencies and defaults may
induce the MFIs to delay in offering individual loans to the borrowers who repay their loans
with a less frequent schedule. On the other hand, a borrower who has a successful repayment
record with a lower repayment frequency relative to an otherwise identical borrower with a
higher repayment frequency has demonstrated that she can handle higher risk, and therefore,
may be eligible to graduate to an individual loan sooner.
<Table 1 here>
Table 1 shows the formal definitions of the independent variables introduced in the analysis.
SAVINGS is measured as a dummy variable that equals one if the borrower has maintained a
non-mandatory savings account with the MFI, and zero otherwise.
SINGLE_BANK_RELATIONSHIP is defined as a dummy variable that equals one if a
borrower has banking relationships with one MFI and zero if she borrows from multiple
MFIs. Ownership of tangible assets (ASSET), such as land, home, livestock etc., is measured
in terms of the market value of assets owned by the borrower’s household divided by the
number of household members. In regression analyses, we use the natural logarithm of one
plus the market value of household assets in order to control the skewness in the ownership of
assets and to include households without any tangible assets. We define large MFIs
17
Empirical evidence provides support of this belief of microfinance practitioners. For example, when BRAC
experimented with moving from weekly to bi-weekly repayment schedule in Bangladesh, delinquencies
increased significantly (Armendariz de Aghion and Morduch, 2010). Satin Credit Care, an urban MFI in north
India, experienced increasing delinquencies when it experimented with a move from daily to weekly repayment
(Fischer and Ghatak, 2011). Field and Pande (2008), however, conducted a randomized controlled experiment
with the clients of the Village Welfare Society in India, and found no significant impact of repayment frequency
on loan repayment rates. Fischer and Ghatak have argued that the loan size in the Field-Pande experiment was,
probably, too small to create any temptations to default.
16
(LARGE_MFI) as those which have more than one hundred thousand active members. We
choose this cutoff value based on the definition of large MFIs provided by the Bangladesh
Microcredit Regulatory Authority (2008).18 Population density (DENSITY) per square
kilometer is estimated at the county level. The data on population density is collected from
the Community Series of the Bangladesh Population Census Report-2001 (Bangladesh
Bureau of Statistics, 2005). Finally, the dummy variable, WEEKLY_REPAYMENT equals
one if the borrower repays loan on a weekly basis, and zero otherwise.
5. Estimation
In this section, we estimate the duration of an uninterrupted repayment record that a
borrower needs to graduate from joint to individual liability loans. The appropriate method to
study durations of any kind is estimating a survival model (see for example, Kiefer, 1988;
Meyer, 1990; and Lancaster, 1990). Following the standard notation of survival analysis
models, let Tj denote the duration of borrower j’s spell with joint liability loan. The
probability that j would graduate to individual loan within a short interval of time, (t, t+dt),
conditional on the fact that she has not graduated as of period t—also known as the hazard19
function—can be calculated as follows:
;
lim
;
(10)
→
Here, X is the vector of covariates that are likely to affect the duration of a spell. In this case,
X includes covariates that may affect the duration of an uninterrupted repayment record that a
borrower needs to graduate to an individual loan, such as the strength of bank-borrower
relationships.
18
Bangladesh Microcredit Regulatory Authority (2008) categorizes the MFIs into five groups based on
borrower outreach: (a) very large MFIs with more than one million active members, (b) large MFIs with more
than hundred thousand but less than a million active borrowers, (c) medium MFIs with more than fifty thousand
but less than hundred thousand members, (d) small MFIs with more than ten thousand but less than fifty
thousand members, and (e) very small MFIs with less than ten thousand active members.
19
It is worth underscoring that the survival analysis model, which owes its origin to medical research, has
primarily been used to examine the factors that affect the duration of life of a cancer patient (see for example,
Collet, 2003). In survival analysis, therefore, it is standard practice to note the conditional probability of an
event (which is the death of a patient) as the “hazard of the event”. Labor economists, for example, used the
term “the hazard of getting employed” while looking at the duration of unemployment (see for example, Meyer,
2001) although getting employed is a positive attribute while hazard has a negative connotation. In the present
study, we used terms, such as, “the hazard of graduation,” and “the risk of graduation” in order to be consistent
with standard notation.
17
To examine the effects of the covariates on the duration of a spell, previous
researchers have used a proportional hazards model, which assumes that the covariates act
multiplicatively on some underlying baseline hazard—the hazard rate when all the covariates
are set equal to zero (see Kiefer (1988) for a review of the applications of survival models).
An important specification issue in a proportional hazards model is the distributional
assumptions regarding duration (or, equivalently, the distributional assumptions regarding the
baseline hazard). The distribution of the hazard may be assumed to be parametric or
nonparametric. A problem with the parametric approach is that there is little theoretical
support for any particular parametric shape of the baseline hazard and, when the assumed
parametric form is incorrect, it inconsistently estimates the covariate effects. On the other
hand, if one uses a nonparametric baseline hazard when a particular parametric form is
appropriate, the resulting estimates are consistent and the loss of efficiency (resulting from
disregarding information about the base line hazard's distribution) may not be very
substantial (Meyer, 1990). Therefore, the use of a nonparametric proportional hazard model
is a reasonable starting point in any survival analysis. Accordingly, we start with estimating
the Cox proportional hazards model (Cox, 1972) in order to estimate the hazard rates and the
factors affecting it. This model asserts the hazard for the jth borrower is as follows:
|
exp
(11)
is the baseline hazard, and the regression coefficients
Here,
are estimated from the
data. The advantage of the Cox model is that it does not require any parameterization of the
baseline hazard, and that no restrictions are imposed about the shape of hazard over time.
We have also used parametric models in order to check whether our results are
sensitive to the choice of a particular assumption regarding the distribution of the baseline
hazard. The two most common distributions used in survival models are the exponential and
Weibull models (Gompers, 1995). The exponential model is the simplest form of parametric
hazard models because it assumes that the baseline hazard is constant. Particularly, in
exponential models, the hazard function is estimated as follows:
|
exp
exp
exp
18
(12)
Here
is some constant. A potential problem with the exponential model is that the hazard
function of such models reflects no duration dependence. 20 In the present case, however, the
likelihood of graduation to individual loans is expected to increase over time as the duration
of repayment record increases, holding everything else equal. Therefore, we expect that the
hazard would reflect positive duration dependence in our data. When the hazard is duration
dependent (either positive or negative), the Weibull distribution fits the model better as it
allows the hazard function to increase or decrease over time (see for example, Meyer, 1990;
Lancaster, 1990; and Gompers, 1995). 21 In the Weibull model, the baseline hazard is
estimated as follows:
(13)
Here, and are ancillary parameters. The hazard function is increasing in duration if
decreasing if
1, and constant if
value of . The value of
1,
1. Duration dependence does not depend on the
depends on the explanatory variables. In the next section, we
report the results of our empirical analyses.
6. Results
An illustration of the pattern of graduation from joint to individual liability loans can
be seen in Table 2, which reports the Kaplan-Meier (KM) estimate of the empirical hazard
rates. The empirical hazard at time t, Ht, is given by the number of borrowers who graduated
at time t, Gt, divided by the number of borrowers who are at risk of graduation, Dt. It is
evident that there are several periods when the empirical hazard is noticeably higher than in
the surrounding periods. Zero hazard rates for the first 12 months imply that no graduation
has occurred until the borrowers complete their first loan cycle. The hazard rates are higher
between 12 and 14 months, and then between 23 and 24 months. It implies that many of the
transitions occur right after the first or the second cycle of joint liability loans. The empirical
hazard rate is the highest at 120 months. But this is due the fact that only a few (6) borrowers
continued their membership with their lenders for 10 years. In other words, at 120 months,
the value of Dt was sufficiently low, which drives the high value of the empirical hazard rate.
20
If the probability of an event increases (decreases) over time, the hazard reflects positive (negative) duration
dependence.
21
In fact, numerous authors have fitted models with a Weibull baseline hazard despite lack of theoretical
support for any particular shape (Meyer, 1990).
19
<Table 2 here>
Table 3 reports the results of our empirical estimation. The results of the Cox
proportional hazards model, exponential model and Weibull model are reported in the second,
third, and fourth columns, respectively. It is evident that both of the relationship variables
have significant positive association with the hazard ratio in all three specifications. In the
Cox proportional hazards estimation, for example, those who maintain a non-mandatory
savings account face a hazard that is more than double of those who do not have such
accounts, and those who bank with a single MFI face a hazard that is 60 percent greater than
those who borrow from multiple MFIs. This implies that when the distributional form of the
baseline hazard is ignored and, a non-parametric estimation model is used, the relationship
variables show a positive impact on the process of graduation from joint to individual loans.
Although the variable, SINGLE_BANKING_RELATIONASHIP, is not statistically
significant, the coefficients associated with the relationship variables in the exponential
model are not substantially different from that in the Cox proportional hazards model.
However, the coefficients associated with the relationship variables increase substantially in
the Weibull model, where the baseline hazard is assumed to be duration dependent. In
particular, according to the Weibull model estimation, those who maintain a non-mandatory
savings account face a hazard more than three times greater than those who do not have such
accounts, and those who bank with a single MFI face a hazard more than four times greater
than those who borrow from multiple MFIs. This is is expected as both of our relationship
variables are likely to vary with time.22 Since Weibull model assumes a duration dependent
baseline hazard, coefficients of time-varying covariates, which especially depend on the time
pattern of the hazard, are more likely to be affected than the coefficients associated with time
consistent covariates (see for example, Meyer, 1990). This is evident from the results
reported in Table 3. Variables that are consistent, at least over a short period of time, such as
size of the MFI and population density of a locality, also do not vary much across
specifications. In sum, however, we argue that our main findings that a strong bank-borrower
relationship expedites the process of graduation in microcredit. The Weibull model which, in
the present context, has a better approximation of the baseline hazard than a non-parametric,
22
As we discuss in the next section, the likelihood of both (a) opening a non-mandatory savings account with an
MFI and (b) maintaining banking relationships with multiple MFIs— increases as the borrower matures over
time.
20
or a duration-independent parametric model, shows the greatest impact of relationship
variables on the process of transition from joint to individual loans.
<Table 3 here>
The results from Table 3 further shows that borrowers who borrow from large MFIs
face a lower hazard of graduation than those who borrow from small MFIs. Thus, borrowers
who borrow from large MFIs need a longer duration of repayment record prior to graduation
to individual loans compared to the borrowers who borrow from small MFIs. This is due to
the fact that extending group loans incurs higher operational costs, and small MFIs are more
inclined to reduce such costs by extending individual loans to their clients (Armendariz de
Aghion and Morduch, 2010). Small MFIs, therefore, offer individual loans to their clients
with relative shorter repayment records. Finally, our results suggest that graduation to
individual loans is fast-tracked in relatively less densely populated regions, where peer
monitoring is costly and imposing social sanctions on defaulting group members is difficult.
6.1. Estimation of Survival Model Using Instrumental Variables
The results presented in Table 3 require a more careful analysis as there might be
potential endogeneity problems in our empirical model. Poor household members in the
developing countries, who are the typical clients of microcredit, always face an enormous
temptation to meet immediate consumption needs (Yunus, 2004). Previous researchers have
defined such behavior as a present bias,23 which is considered as one of the major constraints
to saving in the poor countries (Armendariz de Aghion and Morduch, 2010). Participants in a
microcredit program, however, are contractually required to make regular repayments of
outstanding loans and make regular deposits to mandatory savings accounts at fixed intervals.
These are expected to improve the fiscal discipline of the poor borrowers (Ashraf, Karlan,
and Yin, 2006), and reduce their degree of present bias. Thus, as the duration of membership
with an MFI increases and the borrowers become more disciplined, they tend to hold a
smaller share of their savings at home in order to avoid the temptation of consuming at the
current point in time. This implies that the likelihood of maintaining a non-mandatory
savings account with an MFI is expected to increase with the length of membership, i.e., the
23
Bauer, Chytilova, and Morduch (2010) have conducted framed field experiments in South Indian villages in
order to examine the impact of present bias on economic and financial decision making of the poor households.
One third of the respondents in their sample have shown present bias behavior. See Frederick, Lowenstein, and
O’Donoghue (2002) for a critical review of time inconsistent behavior.
21
duration of uninterrupted repayment records, with the MFI. Therefore, SAVINGS can be an
endogenous variable in our model.
Furthermore, based on evidence from a randomized trial experiment in India,
Banarjee, Duflo, Glennerster, and Kinnan (2010) have shown that the access to microcredit
allows small entrepreneurs expand the size of their businesses. Thus, as the duration of
membership with an MFI increases and the business expands in size, an entrepreneur tends to
demand larger loans in order to meet her increased business demand. But microcredit
programs typically have a low credit ceiling, which often drives mature borrowers to borrow
from multiple sources in order to obtain the required capital. McIntosh et al. (2005) and
McIntosh and Wydick (2005) have identified this as one of the two major reasons of multiple
borrowing in microcredit.24 In the present context, this suggests that the variable
SINGLE_BANK_RELATIONSHIP can also be endogenous: as the length of membership
(i.e., the duration of uninterrupted repayment records) with an MFI increases, the likelihood
of maintaining an association with a single MFI is expected to fall.
In order to overcome these potential endogeneity problems, we use an instrumental
variables technique. An instrumental variables (IV) estimation is made possible by replacing
the endogenous variable with an instrumental variable, which is (a) correlated with the
endogenous variable, (b) uncorrelated with the error term of the estimation model, and (c) not
an explanatory variable in the original equation (Murray, 2006). Condition (c), more
specifically, requires that the instrumental variable should affect the dependent variable only
through its effects on the endogenous (i.e., the excluded) variable. The advantages of using
IV estimation are twofold: it reduces inconsistencies in parameter estimates even in nonlinear models (Angrist, 2008); and it enables drawing causal inferences.25
We have used the exposure to natural disasters as an instrument for SAVINGS.
Particularly, we define the variable NO_DISASTER such that it equals one if the borrower
did not experience natural disasters such as flooding, river erosion, or disordering rain within
the last one year prior to the survey, and zero if the borrower experienced natural disasters.
Exposure to natural disasters causes temporary negative income shocks. Simple consumption
models predict that if households are not credit constrained and if the temporary income
shocks do not substantially affect permanent income, consumption and savings would
respond only marginally. Poor households in developing countries, however, tend to be credit
24
The other major reason for multiple borrowing is the requirement to meet unforeseen consumption demand
especially during the time of crises.
25
Rhodes (2010), for instance, used IV technique to draw causal inferences from survival models.
22
constrained and, therefore, respond significantly to temporary income fluctuations (SchmidtHebbel, Webb and Corsetti, 1992). This suggests that the choice of NO_DISASTER as an
instrumental variable for SAVINGS meets the first criteria of a good IV because
NO_DISASTER is likely to have a significant positive association with SAVINGS. There is,
however, no reason to believe that the length of membership with an MFI can affect the
borrower’s exposure to natural disaster. Thus, the exposure to natural disasters is not
expected to be correlated with the error term of the original equation. Finally, existing
research suggests that when poor borrowers experience temporary income shocks, they draw
down from their savings (Pitt and Khandker, 2002) in order to make repayments of
outstanding loans, which is a prerequisite of continuing membership with an MFI. Thus, we
expect that the exposure to natural disasters can affect the length of membership through a
borrower’s capacity to save money, i.e., the borrower’s likelihood of maintaining a nonmandatory savings account.26
We have used the level of competition among the MFIs in a particular region as an
instrumental variable for SINGLE_BANK_RELATIONSHIP. We measure the degree of
competition in each of the survey locations by the number of households covered by the
PKSF’s partner organizations (COVERAGE). PKSF (Palli Karma-Shahayak Foundation) is
the largest organization in Bangladesh that disburses funds to microfinance institutions.
Currently, 37 percent of the micro-borrowers in Bangladesh receive loans from PKSF’s
partner organizations (Institute for Microfinance, 2010; and PKSF, 2010). Thus, the number
of households covered by the PKSF’s partner organizations, operating in a particular region,
can be used as a reasonably good proxy for the degree of competition. Particularly, a low
value of COVERAGE indicates a high degree of competition among the MFIs in a particular
region. In our empirical analysis, however, we have used the natural logarithm of
COVERAGE. Existing evidence suggests that increased competition among MFIs raises the
incidence of borrowing from multiple MFIs (see for example, McIntosh et al., 2005; and
McIntosh and Wydick, 2005). Thus, we expect that the likelihood of maintaining a banking
relationship with a single MFI falls as the level of competition among MFIs (that is, the
inverse of COVERAGE) increases in a particular region. Thus, COVERAGE fulfills the first
criteria as a good instrumental variable for SINGLE_BANK_RELATIONSHIP. It also
fulfills the second criteria of a good instrument as there is no reason to believe that the level
26
It is worth underscoring that the poor households in the developing countries use a wide range of informal
mechanisms to save. See Rutherford (2000) for a description of such mechanisms. However, for those who are
members of an MFI, non-mandatory savings schemes, offered by the MFI, constitute a major source of
household savings (Ashraf et al., 2006).
23
of competition among the MFIs, which is exogenously determined by the factors related to
the institutional and industrial organization of the microcredit sector in a particular region,
can be affected by an individual borrower’s length of membership with an MFI. McIntosh et
al. further show that multiple memberships, followed by increased competition, display
increased over-indebtedness and default rates in the microcredit sector. Since default on a
loan obligation terminates membership with the MFI, it can be argued that increased
competition among the MFIs can reduce the length of membership through increasing the
likelihood of multiple borrowing and over-indebtedness.
Following Angrist and Pischke (2009) and Abbring and van den Berg (2005), Rhodes
(2010) suggests a simple procedure to estimate the survival model using instrumental
variables. The first step is to test for the strength of the instruments. This can be done by
regressing the endogenous variables—the maintenance of a non-mandatory savings account
and single banking relationship—on the exogenous and instrumental variables, using a logit
or probit model. Although there is no absolute test for the strength of an instrument, a
significant association between the endogenous and instrumental variables is indicative of the
strength of the instrument. We use logit models to check for the strength of our instruments.
The results are reported in Table 4. It is evident that (a) borrowers who did not experience
any natural disaster are 21 percentage points more likely to have a non-mandatory savings
account than those who experienced a natural disaster (this association is statistically
significant at the five percent level); and (b) a one unit increase in the value of (the natural
logarithm of) COVERAGE raises the likelihood of maintaining an association with a single
MFI by 17 percentage points (this association is statistically significant at the one percent
level).
<Table 4 here>
The second step is to estimate the survival model using the exogenous and
instrumental variables as explanatory variables. This is similar to the estimation of the
reduced form equation in a two-stage least squares model. The results of this survival model
are presented in Table 5. It is evident that those who have a non-mandatory savings account
face a significantly greater hazard of graduation than those who do not have such accounts
with the MFI; and those who borrow from one MFI face a significantly greater hazard of
graduation than those who borrow from multiple sources. The results are robust across a
range of non-parametric and parametric specifications. Thus, our main results—that
borrowers with a strong banking relationship graduate sooner from joint to individual liability
24
loans than those who do not have a strong relationship with the MFI—also hold true in the
instrumental variables estimation.
<Table 5 here>
Rhodes (2010) has, however, suggested that an additional step is needed in order to
draw causal inferences from survival analysis using instrumental variables. Following his
suggestion, we estimated the hazard rate at a given point in time based on the survival model
that uses exogenous variables and the instrumental variables as explanatory variables. The
estimated hazard rates are then regressed on the probability of maintaining a non-mandatory
savings account and the probability of maintaining a relationship with a single bank, using an
ordinary least squares method. Particularly, we estimated the hazard rates from the
exponential and Weibull models. The probabilities of maintaining a non-mandatory savings
account and maintaining a relationship with a single bank are estimated based on logit models.
The results of the OLS regression are presented in Table 6. It is evident that the coefficients
with both the probabilities of maintaining a non-mandatory savings account and maintaining
a relationship with a single bank are statistically significant at the one percent level in both
specifications. This implies that the association between bank-borrower relationships and the
process of transition from joint to individual liability loans is not merely a correlation. Rather,
one can reasonably argue that a strong bank-borrower relationship expedites the process of
graduation from joint to individual liability loans.
<Table 6 here>
7. Concluding Remarks
Existing research suggests that borrowers have to establish a good reputation in the
credit market, by repaying loans, in order to enjoy flexibilities in loan contracts (Diamond,
1991; and Boot and Thakor, 1994). One common form of providing flexibilities in
microcredit contracts is to remove the joint liability clause (Navajas et al., 2003). Borrowers
who have established a good reputation by repaying loans use their loans with more prudence
without any peer pressure in order to protect valuable reputational capital. As a result, MFIs
can offer individual loans to these borrowers without increasing their credit risks. In this
paper, we show that the strength of bank-borrower relationships affects the duration of a
repayment record that a borrower requires to graduate from joint to individual liability loans.
Particularly, the results of our empirical analysis show that borrowers (a) who maintain a
25
non-mandatory savings account with the MFI, and (b) who borrow from a single MFI,
receive individual loans with relatively shorter repayment records.
There is widespread consensus among researchers and practitioners in that
maintaining repeat borrowers is critical for the long run financial viability of the MFIs (see
for example, Wright, 2000 and 2001; and Meyer, 2002). Repeat borrowing reduces
administrative costs and lowers default risks. Thus, MFIs have a clear incentive to protect
voluntary drop out by their mature borrowers. Existing studies further suggest that the
presence of joint liability is a major driver of voluntary drop outs in the microcredit sector as
it creates excessive tensions among group members (ASA, 1996; and Women’s World
Banking, 2003). The results of our empirical analysis, therefore, have important implications
for microfinance practitioners. Particularly, our results imply that MFIs should invest more in
producing relationship driven information. Such information would help expedite the process
of a borrower’s graduation from a joint to an individual liability loan which, in turn, would
reduce voluntary drop outs by otherwise creditworthy borrowers.
26
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Table 1
Operational Definitions of the Variables and Descriptive Statistics
Variable
Definitions
SAVINGS
1 if the borrower maintains a nonmandatory savings account; 0 otherwise
SINGLE_BANK_RELATIONSHIP
1 if the borrower borrows from a single
MFI; 0 if she borrows from multiple
MFIs
ASSET
Market value of household assets
divided by the number of household
members
LARGE_MFI
1 if the corresponding MFI has more
than one hundred thousand active
borrowers; 0 otherwise.
DENSITY
Population density at the county level
per square kilometer.
WEEKLY_REPAYMENT
1 if the borrower repays her loan on a
weekly basis, and zero otherwise
32
Table 2
Graduations, Censorings, and the Kaplan-Meier Empirical Hazard
Duration of
repayment
record
(months)
T
1
2
3
4
5
6
8
10
11
12
13
14
15
16
18
22
23
24
25
30
32
36
45
48
60
66
72
84
90
108
120
Number of
borrowers at risk
of graduation
Dt
334
322
296
286
280
276
253
248
246
243
189
173
128
116
99
84
79
78
44
43
41
40
30
29
21
18
16
11
9
7
6
Number of
graduation at
time t
Gt
0
0
0
0
0
0
0
0
0
6
15
22
8
7
3
0
1
11
1
1
0
2
0
3
0
0
1
0
0
0
1
33
Number of
censored
observations at t
Ct
12
26
10
6
4
23
5
2
3
48
1
23
4
10
12
5
0
23
0
1
1
8
1
5
3
2
4
2
2
1
5
Hazard
rate
Ht
0
0
0
0
0
0
0
0
0
0.024
0.079
0.127
0.062
0.06
0.03
0
0.012
0.141
0.022
0.023
0
0.05
0
0.103
0
0
0.0625
0
0
0
0.166
Table 3
Hazard of Graduation from Joint to Individual Liability Loans
Cox Proportional
Hazard Model
Exponential
Model
Hazard
ratio
Hazard
ratio
Hazard ratio
2.235***
2.435***
3.176***
SINGLE_BANK_RELATIONSHIP
1.605*
1.486**
4.112***
ASSET
0.980
0.972
0.961*
LARGE_MFI
0.513***
0.558**
0.471***
DENSITY
0.999***
0.999***
0.998**
WEEKLY_REPAYMENT
Log-likelihood
Chi-square
p-value
0.108
-378.710
28.01
0.000
1.019
-188.890
30.22
0.000
1.642
-166.192
63.72
0.000
0.535 (SE =
0.041)
Explanatory variables
SAVINGS
Α
* significant at 0.1 level, ** significant at 0.05 level, *** significant at 0.01 level
34
Weibull Model
Table 4
Estimating the Strength of the Instrumental Variables
Dependent variable:
SAVINGS
Dependent variable:
SINGLE_BANK_RELATIONSHIP
Explanatory variables
Marginal Effects
Marginal Effects
NO_DISASTER
0.218**
0.099
COVERAGE
0.080
0.169***
ASSET
-0.001
0.007*
LARGE_MFI
0.032
0.075*
DENSITY
0.001***
0.001
WEEKLY_REPAYMENT
-0.043
-0.037
Log-likelihood
Chi-square
p-value
-201.114
15.18
0.03
-134.969
32.11
0.07
* significant at 0.1 level, ** significant at 0.05 level, *** significant at 0.01 level
35
Table 5
Hazard of Graduation Using Instrumental Variables
Cox
Proportional
Hazard Model
Exponential
Model
Weibull
Model
Hazard
Ratio
Hazard
Ratio
Hazard
Ratio
2.213**
2.243***
3.094***
2.001***
2.241**
3.471***
ASSET
0.994
0.978
0.981
LARGE_MFI
0.596**
0.639**
0.636**
DENSITY
0.999
0.999
0.999
WEEKLY_REPAYMENT
Log-likelihood
0.856
-379.601
0.829
-188.157
0.734
-176.691
Chi-square
26.23
31.64
-42.71
p-value
0.002
0.000
0.000
Explanatory variables
SAVINGSa
SINGLE_BANK_RELATIONSHIP
b
1.474 (SE
= 0.104)
Α
* significant at 0.1 level, ** significant at 0.05 level, *** significant at 0.01 level
a. estimated by instrumental variable, NO_DISASTER
b. estimated by instrumental variable, COVERAGE
36
Table 6
Regression of the Estimated Probability of Graduation on the Probability of Maintaining
Non-Mandatory Savings and the Probability of Single Banking Relationship
Dependent variable:
Probability of Graduation
Estimated by the Exponential
Model
Dependent variable:
Probability of Graduation
Estimated by the Weibull
Model
Explanatory variables
OLS coefficients
OLS coefficients
Probability of Maintaining
Non-Mandatory Savings
3.061***
3.593***
Probability of Single Banking
Relationship
1.845***
3.016***
Constant
-17.56
-23.72
Adjusted R
0.56
0.62
F (2, 331)
211.33
265.39
p-value
0.000
0.000
2
* significant at 0.1 level, ** significant at 0.05 level, *** significant at 0.01 level
37
APPENDIX
Suppose there are three members in a borrowing group: Max, Mop, and Min, all of whom
invest in a safe project. The following table shows all possible combinations of borrower
Max’s payoff under the assumption that the Max’s project outcome is independently
distributed of that of Mop and Min.
Table A: Calculation of Expected Payoff in a Group of Three Borrowers
Project outcome
of Max
Success
Project outcome
of Mop
Success
Project outcome
of Min
Success
Likelihood of the
event
PS.PS.PS
Max’s payoff
Success
Success
Failure
PS.PS.(1-PS)
YS-r+V-(c/2)
Success
Failure
Success
PS.(1-PS).PS
YS-r+V-(c/2)
Success
Failure
Failure
PS.(1-PS)(1-.PS)
YS-r+V-2c
Failure
Success
Success
(1-PS).PS.PS
V
Failure
Success
Failure
(1-PS).PS.(1-PS)
V
Failure
Failure
Success
(1-PS).(1-PS).PS
V
Failure
Failure
Failure
(1-PS).(1-PS).(1-PS)
0
YS-r+V
Max’s expected payoff can, therefore, be calculated from the table as follows:
US, MAX =
PS [PS2 (YS-r+V) + 2 PS (1- PS) (YS-r+V-(c/2)) + (1-PS2) (YS-r+V-2c)]
+ (1-PS) [PS2 (V) + 2PS (1-PS) (V)]
The same condition can be directly derived from equation (3).
38